London or Manchester?

Neither city is made for a beach vacation, but London has the better seaside within reach. Brighton is about an hour by train, with a pebble beach, a pier and a promenade, and Margate and Whitstable have sandier shores for a breezy day out. London's lidos at Brockwell Park and Parliament Hill, and the Hampstead Heath ponds, give it a real outdoor swimming culture.

Manchester has nothing like that in the city. The dunes and pinewoods at Formby and the promenade at Blackpool make a pleasant coastal walk, but few people swim in the Irish Sea. An indoor pool is the realistic option.

London is one of the great eating cities, and its range comes from its communities: Bangladeshi cooking on Brick Lane, Punjabi food in Southall, Turkish grills on Green Lanes, and Caribbean and West African kitchens south of the river. A large fine-dining scene and Borough Market add to that. Few visitors run out of new things to try in a week.

Manchester covers less ground but does it cheaply and well. It has one of Britain's larger Chinatowns, the South Asian restaurants of Wilmslow Road in Rusholme, and food halls in old Ancoats mills. Fine dining is thin. Drinking is where it holds its own, from Victorian pubs to breweries under the railway arches.

This is where the two cities differ most. London has the British Museum, the National Gallery, the V&A, the two Tates and the Natural History Museum, most of them free, as well as the Tower, Westminster Abbey and St Paul's. A week there barely scratches the surface.

Manchester's sights tell one story, that of the first industrial city. You see it in the neo-Gothic Town Hall, the John Rylands Library, the mills of Castlefield and Ancoats, and the Science and Industry Museum. The Pre-Raphaelites at the Manchester Art Gallery and the Whitworth are worth seeing, but two days cover the essentials.

London has more and bigger nights out because it is really several scenes. Soho has cocktail bars and a late street crowd, Shoreditch and Dalston have clubs and warehouse parties, and Brixton and Peckham have large venues and rooftop bars. The downsides are the distances between districts and the pubs that still empty around eleven.

Manchester packs its nightlife into a small centre that is easy to explore on foot. The Northern Quarter's basement bars and DJ rooms, the Gay Village on Canal Street and the city's dance-music history give it real character. Students keep it busy midweek in term time. It goes quieter in summer, and the autumn and winter warehouse raves are the high point.

Manchester has the edge for anyone who wants proper hills. The Peak District's gritstone edges and moorland begin on its eastern fringe, the West Pennine Moors lie to the north, and the Lake District is about an hour and a half by train. Heaton Park and the canal towpaths out of Castlefield are there for gentler days.

London is greener within the city, with the deer of Richmond Park, the views from Hampstead Heath and the gardens at Kew. The countryside around it is gentle, though: the Chilterns and the South Downs have good footpaths but nothing wild. Manchester's wetter weather is the trade-off.

Both cities sit at the hub of a rail network, so day trips are easy from either. London's list is longer and more famous: Oxford, Cambridge, Windsor Castle, Bath, Stonehenge with Salisbury, and Canterbury. That is enough for several very different outings in one week.

Manchester's outings are northern and often more rural. Liverpool and Chester are about an hour away and York about an hour and a half. Chatsworth, Buxton and the Lake District towns combine stately homes and landscape. It is a strong list, just with fewer famous names.

London is the easier city in which to fill a week with children, and much of it is free: the dinosaurs at the Natural History Museum, the Science Museum, the Young V&A and the pirate ship at the Diana Memorial Playground. There is also the zoo in Regent's Park, with Legoland and the Harry Potter studio tour outside the city. The drawbacks are the long distances and the Tube stairs, which are hard with a buggy.

Manchester has good free museums for a day or two, including the working engines at the Science and Industry Museum and the vivarium at the Manchester Museum. The aquarium and indoor snow slope at the Trafford Centre help when it rains. Its biggest draws, Chester Zoo and Alton Towers, each need a full day out.

London's transport is more complete. The Underground, the Elizabeth line, the buses and the Thames riverboats reach almost everywhere, all on one contactless payment. The cost is scale: journeys between neighbourhoods are long, and trains are packed at rush hour.

Manchester asks less of its transport because the centre is compact and flat, and most sights are within walking distance of each other. The Metrolink trams serve Salford Quays, Old Trafford and the airport, but beyond the centre you rely more on buses, and rain often makes walking less pleasant.

London is worth a trip for shopping alone. It has the luxury houses of Bond Street, the bespoke tailors of Savile Row, Liberty, Harrods and Fortnum & Mason, and then Portobello Road's antiques, the Columbia Road flower market and the bookshops of Charing Cross Road.

Manchester is the main shopping city of the north, but its range is broad rather than special. The Northern Quarter, with Afflecks, record shops and vintage clothing, is the part with personality. The high-street core and the Trafford Centre offer what most large cities do, with less at the luxury end.

London is the harder city on the wallet, and most of the cost lands on where you sleep and how you spend your evenings. A central base is the biggest single expense, which is why many visitors stay further out along a good Tube or rail line and accept the longer ride in. Single fares are steep, but the daily cap on contactless payment means a day of hopping between sights costs no more than a few journeys. Lunch at a market or a Turkish or South Asian café keeps the daytime spending down.

Manchester is noticeably cheaper overall, and its compact centre saves money in a quieter way. Most of what a visitor wants is within walking distance, so transport hardly figures in the budget. The cost to watch is timing: a home match at Old Trafford or the Etihad, an arena concert or a large conference pushes room rates up sharply, so the same stay can cost very different amounts from one week to the next. Eating out and pub drinks cost what they do in most British cities, so the savings come from the room and the travel rather than the table.

London is in a different league for theatre and classical music. It has the West End, the National Theatre, the Globe, the Royal Court, the Royal Opera House and five major orchestras, so there is serious choice every night.

Manchester's strength is live music. Its gig circuit runs from back rooms in the Northern Quarter to one of Europe's largest indoor arenas, and the Hallé and the BBC Philharmonic play at the Bridgewater Hall. The Royal Exchange's theatre-in-the-round is worth seeing for the building alone. There is no resident opera company, and touring West End musicals play at the Palace and the Opera House.

Neither is a restful city, but London offers more to a visitor who wants to unwind. Its surviving Turkish baths in Bayswater and at Ironmonger Row, with steam rooms and plunge pools under tiled vaults, offer real bathing, and the grand hotels of Mayfair and Knightsbridge run full spas. Bath's thermal waters are a manageable day trip.

Manchester has no bathing tradition. Victoria Baths is a heritage visit rather than a swim, and wellness means hotel and day spas. The best escape is the train to Buxton or out into the Peak District.